There is definitely one son of Craster who became a White Walker. Craster's Last Son was given to the White Walkers in Season 4 Episode 4 and, when touched by the Night's King acquired the deep blue eyes of the Others. While this was probably the fate of his other sons that is not certain.
Is there some kind of magical connection between the White Walkers and Craster?
Beyond the fact that he sacrificed his sons to them and at least one became a White Walker? Not known.
Now that Craster is dead, there are no more boys being groomed to become White Walkers.
I think this is too long a bow to draw. The White Walkers have been in existence for thousands of years; whether they are immortal or needed to procreate during that time is not known. There may have been and still might be others like Craster who sacrifice their sons to preserve their own lives.
Or, anyone that is alive can be changed into a White Walker?
Is it valid to ask if wildings are more afraid of becoming a wight or a White Walker?
Of course it's valid to ask. I don't know the answer.